You don’t choose a sorcery card when Quicken resolves. Rather, this sets up a rule that is true for you until the turn ends or until you cast a sorcery card, even if you cast that sorcery at a time you normally could.

2/1/2006

If you cast multiple Quickens on the same turn, they’ll all apply to the very next sorcery spell you cast.

9/25/2006

After Quicken resolves, you can Suspend a sorcery in your hand any time you can cast an instant. As soon as you actually cast a sorcery, you lose this capability.

7/1/2013

Casting a copy of a sorcery card won’t “use up” Quicken’s effect because the copy isn’t a card.